Given the linear correlation coefficient r and the sample size n, determine the critical values or r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of .05. r = .898, n = 9 а. Critical values: r = -.666, no significant linear correlation b. Critical values: r = .666, no significant linear correlation с. Critical values: r = +.666, significant linear correlation d. Critical values: r = 1.666, no significant linear correlation

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Given the linear correlation coefficient \( r \) and the sample size \( n \), determine the critical values of \( r \) and use your finding to state whether or not the given \( r \) represents a significant linear correlation. Use a significance level of 0.05.

\[ r = 0.898, \, n = 9 \]

a. Critical values: \( r = -0.666 \), no significant linear correlation

b. Critical values: \( r = 0.666 \), no significant linear correlation

c. Critical values: \( r = \pm 0.666 \), significant linear correlation

d. Critical values: \( r = \pm 0.666 \), no significant linear correlation

**Explanation:**

The task is to compare the given correlation coefficient \( r = 0.898 \) with the critical values to determine if there is a significant linear correlation. The significance level is set at 0.05, meaning there is a 5% risk of concluding that a correlation exists when there is none.

For example, in option c, the critical values for \( r \) are \( \pm 0.666 \). Since \( 0.898 \) is greater than \( 0.666 \), it is considered a significant linear correlation.
Transcribed Image Text:Given the linear correlation coefficient \( r \) and the sample size \( n \), determine the critical values of \( r \) and use your finding to state whether or not the given \( r \) represents a significant linear correlation. Use a significance level of 0.05. \[ r = 0.898, \, n = 9 \] a. Critical values: \( r = -0.666 \), no significant linear correlation b. Critical values: \( r = 0.666 \), no significant linear correlation c. Critical values: \( r = \pm 0.666 \), significant linear correlation d. Critical values: \( r = \pm 0.666 \), no significant linear correlation **Explanation:** The task is to compare the given correlation coefficient \( r = 0.898 \) with the critical values to determine if there is a significant linear correlation. The significance level is set at 0.05, meaning there is a 5% risk of concluding that a correlation exists when there is none. For example, in option c, the critical values for \( r \) are \( \pm 0.666 \). Since \( 0.898 \) is greater than \( 0.666 \), it is considered a significant linear correlation.
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